Time Undersampled Acquisition for Multidimensional Sparse Signals With Application to Magnetic Resonance Spectroscopic Imaging

This paper deals with acceleration of multidimensional signal acquisition. The signal is assumed to have multiple discrete spatial dimensions where each point is time varying. The one-dimensional Fourier transform of the time evolution of each point is assumed to have an
a priori
known bounded support. The Fourier transform of the spatial domain is divided into several partitions, each of which can be sequentially acquired over time. We propose a method for undersampling the time dimension that enables interleaving of the samples hence speeding up signal acquisition. This method, applied to realistic simulated magnetic resonance spectroscopic imaging data (MRSI), leads to a reduction in the acquisition time by a factor of three.